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Coupled Systems Mechanics
  Volume 1, Number 2, June 2012 , pages 155-163

Analytical approximate solution for Initial post-buckling behavior of pipes in oil and gas wells
Yongping Yu, Youhong Sun and Yucen Han

    This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton\'s method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to \"reference\" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.
Key Words
    analytical approximation; buckling; shooting method
Yongping Yu and Youhong Sun : College of Construction Engineering, Jilin University, Changchun 130021, P.R. China
Yucen Han : School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P.R. China

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